【智能优化算法】基于分段权重和变异反向学习的蝴蝶优化算法求解单目标优化问题附matlab代码

1 简介

针对原始蝴蝶优化算法容易陷入局部最优解,收敛速度慢及寻优精度低等问题,提出分段权重和变异反向学习的蝴蝶优化算法.通过飞行引领策略来矫正邻域内蝴蝶的自身飞行,降低盲目飞行,增强算法跳出局部最优的能力;引入分段权重来平衡全局勘探及局部开发的能力,进而实现蝴蝶位置动态更新;使用变异反向学习对位置进行扰动,增加种群多样性以及提高算法的收敛速度.通过对9个测试函数和部分CEC2014函数及Wilcoxon秩和检验来评估改进算法的寻优能力,实验结果表明改进算法的收敛速度及寻优精度得到了极大改进.

2 部分代码

%% Monarch Butterfly Optimization (MBO)

% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %%

%% Notes:

% Different run may generate different solutions, this is determined by

% the the nature of metaheuristic algorithms.

function [MinCost] = MBO(ProblemFunction, DisplayFlag, RandSeed)

% Monarch Butterfly Optimization (MBO) software for minimizing a general function

% The fixed Function Evaluations (FEs) is considered as termination condition.

% INPUTS: ProblemFunction is the handle of the function that returns

% the handles of the initialization, cost, and feasibility functions.

% DisplayFlag = true or false, whether or not to display and plot results.

% ProbFlag = true or false, whether or not to use probabilities to update emigration rates.

% RandSeed = random number seed

% OUTPUTS: MinCost = array of best solution, one element for each generation

% Hamming = final Hamming distance between solutions

% CAVEAT: The "ClearDups" function that is called below replaces duplicates with randomly-generated

% individuals, but it does not then recalculate the cost of the replaced individuals.

tic

if ~exist('ProblemFunction', 'var')

ProblemFunction = @Ackley;

end

if ~exist('DisplayFlag', 'var')

DisplayFlag = true;

end

if ~exist('RandSeed', 'var')

RandSeed = round(sum(100*clock));

end

[OPTIONS, MinCost, AvgCost, InitFunction, CostFunction, FeasibleFunction, ...

MaxParValue, MinParValue, Population] = Init(DisplayFlag, ProblemFunction, RandSeed);

nEvaluations = OPTIONS.popsize;

% % % % % % % % % % % % Initial parameter setting % % % % % % % % % % % %%%%

%% Initial parameter setting

Keep = 2; % elitism parameter: how many of the best habitats to keep from one generation to the next

maxStepSize = 1.0; %Max Step size

partition = OPTIONS.partition;

numButterfly1 = ceil(partition*OPTIONS.popsize); % NP1 in paper

numButterfly2 = OPTIONS.popsize - numButterfly1; % NP2 in paper

period = 1.2; % 12 months in a year

Land1 = zeros(numButterfly1, OPTIONS.numVar);

Land2 = zeros(numButterfly2, OPTIONS.numVar);

BAR = partition; % you can change the BAR value in order to get much better performance

% % % % % % % % % % % % End of Initial parameter setting % % % % % % % % % % % %%

% % % % % % % % % % % % Begin the optimization loop % % % % % % % % % %%%%

% Begin the optimization loop

GenIndex = 1;

% for GenIndex = 1 : OPTIONS.Maxgen

while nEvaluations< OPTIONS.MaxFEs

% % % % % % % % % % % % Elitism Strategy % % % % % % % % % % % %%%%%

%% Save the best monarch butterflis in a temporary array.

for j = 1 : Keep

chromKeep(j,:) = Population(j).chrom;

costKeep(j) = Population(j).cost;

end

% % % % % % % % % % % % End of Elitism Strategy % % % % % % % % % % % %%%%

% % % % % % % % % % % % Divide the whole population into two subpopulations % % % %%%

%% Divide the whole population into Population1 (Land1) and Population2 (Land2)

% according to their fitness.

% The monarch butterflis in Population1 are better than or equal to Population2.

% Of course, we can randomly divide the whole population into Population1 and Population2.

% We do not test the different performance between two ways.

for popindex = 1 : OPTIONS.popsize

if popindex <= numButterfly1

Population1(popindex).chrom = Population(popindex).chrom;

else

Population2(popindex-numButterfly1).chrom = Population(popindex).chrom;

end

% % % % % % % % % % % End of Divide the whole population into two subpopulations % % %%%

% % % % % % % % % % % %% Migration operator % % % % % % % % % % % %%%%

%% Migration operator

for k1 = 1 : numButterfly1

for parnum1 = 1 : OPTIONS.numVar

r1 = rand*period;

if r1 <= partition

r2 = round(numButterfly1 * rand + 0.5);

Land1(k1,parnum1) = Population1(r2).chrom(parnum1);

else

r3 = round(numButterfly2 * rand + 0.5);

Land1(k1,parnum1) = Population2(r3).chrom(parnum1);

end

end %% for parnum1

NewPopulation1(k1).chrom = Land1(k1,:);

end %% for k1

% % % % % % % % % % % %%% End of Migration operator % % % % % % % % % % % %%%

% % % % % % % % % % % % Evaluate NewPopulation1 % % % % % % % % % % % %%

%% Evaluate NewPopulation1

SavePopSize = OPTIONS.popsize;

OPTIONS.popsize = numButterfly1;

% Make sure each individual is legal.

NewPopulation1 = FeasibleFunction(OPTIONS, NewPopulation1);

% Calculate cost

NewPopulation1 = CostFunction(OPTIONS, NewPopulation1);

% the number of fitness evaluations

nEvaluations = nEvaluations + OPTIONS.popsize;

OPTIONS.popsize = SavePopSize;

% % % % % % % % % % % % End of Evaluate NewPopulation1 % % % % % % % % % % % %%

% % % % % % % % % % % % Butterfly adjusting operator % % % % % % % % % % % %%

%% Butterfly adjusting operator

for k2 = 1 : numButterfly2

scale = maxStepSize/(GenIndex^2); %Smaller step for local walk

StepSzie = ceil(exprnd(2*OPTIONS.Maxgen,1,1));

delataX = LevyFlight(StepSzie,OPTIONS.numVar);

for parnum2 = 1:OPTIONS.numVar,

if (rand >= partition)

Land2(k2,parnum2) = Population(1).chrom(parnum2);

else

r4 = round(numButterfly2*rand + 0.5);

Land2(k2,parnum2) = Population2(r4).chrom(1);

if (rand > BAR) % Butterfly-Adjusting rate

Land2(k2,parnum2) = Land2(k2,parnum2) + scale*(delataX(parnum2)-0.5);

end

end %% for parnum2

NewPopulation2(k2).chrom = Land2(k2,:);

end %% for k2

% % % % % % % % % % % % End of Butterfly adjusting operator % % % % % % % % % % % %

% % % % % % % % % % % % Evaluate NewPopulation2 % % % % % % % % % % % %%

%% Evaluate NewPopulation2

SavePopSize = OPTIONS.popsize;

OPTIONS.popsize = numButterfly2;

% Make sure each individual is legal.

NewPopulation2 = FeasibleFunction(OPTIONS, NewPopulation2);

% Calculate cost

NewPopulation2 = CostFunction(OPTIONS, NewPopulation2);

% the number of fitness evaluations

nEvaluations = nEvaluations + OPTIONS.popsize;

OPTIONS.popsize = SavePopSize;

% % % % % % % % % % % % End of Evaluate NewPopulation2 % % % % % % % % % % % %%

% % % % % % % Combine two subpopulations into one and rank monarch butterflis % % % % % %

%% Combine Population1 with Population2 to generate a new Population

Population = CombinePopulation(OPTIONS, NewPopulation1, NewPopulation2);

% Sort from best to worst

Population = PopSort(Population);

% % % % % % End of Combine two subpopulations into one and rank monarch butterflis % %% % %

% % % % % % % % % % % % Elitism Strategy % % % % % % % % % % % %%% %% %

%% Replace the worst with the previous generation's elites.

n = length(Population);

for k3 = 1 : Keep

Population(n-k3+1).chrom = chromKeep(k3,:);

Population(n-k3+1).cost = costKeep(k3);

end % end for k3

% % % % % % % % % % % % End of Elitism Strategy % % % % % % % % % % % %%% %% %

% % % % % % % % % % Precess and output the results % % % % % % % % % % % %%%

% Sort from best to worst

Population = PopSort(Population);

% Compute the average cost

[AverageCost, nLegal] = ComputeAveCost(Population);

% Display info to screen

MinCost = [MinCost Population(1).cost];

AvgCost = [AvgCost AverageCost];

if DisplayFlag

disp(['The best and mean of Generation # ', num2str(GenIndex), ' are ',...

num2str(MinCost(end)), ' and ', num2str(AvgCost(end))]);

end

% % % % % % % % % % % End of Precess and output the results %%%%%%%%%% %% %

%% Update generation number

GenIndex = GenIndex+1;

end % end for GenIndex

Conclude2(DisplayFlag, OPTIONS, Population, nLegal, MinCost, AvgCost);

toc

% % % % % % % % % % End of Monarch Butterfly Optimization implementation %%%% %% %

function [delataX] = LevyFlight(StepSize, Dim)

%Allocate matrix for solutions

delataX = zeros(1,Dim);

%Loop over each dimension

for i=1:Dim

% Cauchy distribution

fx = tan(pi * rand(1,StepSize));

delataX(i) = sum(fx);

end

3 仿真结果

4 参考文献

[1]李守玉,何庆,杜逆索. 分段权重和变异反向学习的蝴蝶优化算法[J]. 计算机工程与应用, 2021, 57(22):10.

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